First unified benchmark finds GLR family has only 3x median slowdown over LR(1) on deterministic grammars and is the fastest among generalized parsers.
Strassen , Gaussian elimination is not optimal , Numerische Mathematik, 13 (1969), pp
9 Pith papers cite this work, alongside 2,528 external citations. Polarity classification is still indexing.
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For matrix multiplication ⟨d,n,d⟩ the round complexity is Õ(d^{4/3}); for ⟨n,d,n⟩ it is Θ(d √n) when d ≤ √n and O(d^{2/3} n^{2/3}) when d ≥ √n.
General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
Blocked Jacobi attains the communication lower bound for classical O(n^3) matrix multiplication while a recursive version reaches near-optimal arithmetic and communication cost using fast Strassen-like multiplication; analogous bounds hold for one-sided Jacobi SVD.
FalconGEMM delivers a framework with deployment, group-parallel execution, and analytical decision modules that makes lower-complexity matrix multiplication practical, beating cuBLAS and similar libraries by 7.59-17.85% on LLM tasks.
Approximates large matrix multiplication via truncated SVD and circulant decompositions with O(n^2 log n) complexity and ~1% relative error, including LLM operation demonstrations.
Empirical benchmarking study comparing execution time, user time, CPU time, and MAC efficiency of established matrix multiplication algorithms on hardware for varying matrix sizes.
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An Empirical Comparison of General Context-Free Parsers
First unified benchmark finds GLR family has only 3x median slowdown over LR(1) on deterministic grammars and is the fastest among generalized parsers.
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Rectangular Matrix Multiplication in the Low-Bandwidth Model
For matrix multiplication ⟨d,n,d⟩ the round complexity is Õ(d^{4/3}); for ⟨n,d,n⟩ it is Θ(d √n) when d ≤ √n and O(d^{2/3} n^{2/3}) when d ≥ √n.
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Asymptotic Rank Speedup Theorems, Revisited
General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
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Minimizing the Arithmetic and Communication Complexity of Jacobi's Method for Eigenvalues and Singular Values: Part One -- Serial Algorithms
Blocked Jacobi attains the communication lower bound for classical O(n^3) matrix multiplication while a recursive version reaches near-optimal arithmetic and communication cost using fast Strassen-like multiplication; analogous bounds hold for one-sided Jacobi SVD.
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FalconGEMM: Surpassing Hardware Peaks with Lower-Complexity Matrix Multiplication
FalconGEMM delivers a framework with deployment, group-parallel execution, and analytical decision modules that makes lower-complexity matrix multiplication practical, beating cuBLAS and similar libraries by 7.59-17.85% on LLM tasks.
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Efficient approximations of matrix multiplication using truncated decompositions
Approximates large matrix multiplication via truncated SVD and circulant decompositions with O(n^2 log n) complexity and ~1% relative error, including LLM operation demonstrations.
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MAC Performance and Algorithmic Optimization in Matrix Multiplication Workloads
Empirical benchmarking study comparing execution time, user time, CPU time, and MAC efficiency of established matrix multiplication algorithms on hardware for varying matrix sizes.
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